Behavior and Modeling of Existing Reinforced Concrete Columns Kenneth J. Elwood University of British Columbia with contributions from Terje Haukaas, UBC Jose Pincheira, Univ of Wisconsin John Wallace, UCLA

Questions? What is the stiffness of the column? What is the strength of the column? What failure mode is expected? What is the drift capacity… at shear failure? at axial failure? How can we account for uncertainty in the models? How can we model this behavior for the analysis of a structure? What is the influence of poor lap splices?

Column response Effective Stiffness Strength Drift Capacities

Effective stiffness FEMA 356

Effective stiffness Flexural Deformations: fy Does not account for end rotations due to bar slip! L fy

Effective stiffness Slip Deformations: L u dslip = ½ eyl C T=Asfy l u bond stress steel stress steel strain u l L u fy ey dslip = ½ eyl C T=Asfy

Effective stiffness Modeling options: L Option 1 (with slip springs) Stiffness based on moment-curvature analysis (or FEMA 356 recommendations) L Slip springs:

Effective stiffness Modeling options: L Option 2 (without slip springs): Use effective stiffness determined from column tests. More flexible than FEMA recommendations for low axial load. L

Effective stiffness FEMA 356

Yield displacement

Column response Effective Stiffness Strength Drift Capacities

Shear Strength Several models available to estimate shear strength: Aschheim and Moehle (1992) Priestley et al. (1994) Konwinski et al. (1995) FEMA 356 (Sezen and Moehle, 2004) ACI 318-05 All models (except ACI) degrade shear strength with increasing ductility demand.

Shear Strength Based on principle tensile stress exceeding ft = 6 fn (fn, vc) fn vc = ft + 1 k c V = ÷ ø ö d a ç è æ 1 g 0.8Ag A f P + ' 6 Based on principle tensile stress exceeding ft = 6 c f ' Sezen and Moehle, 2004

Shear Strength d a Based on principle tensile stress exceeding ft = 6 k c V = ÷ ø ö d a ç è æ 1 g 0.8Ag A f P + ' 6 Based on principle tensile stress exceeding ft = 6 c f ' Accounts for degradation due to flexural and bond cracks Sezen and Moehle, 2004

Displacement Ductility Shear Strength 0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 Displacement Ductility k k c V = ÷ ø ö d a ç è æ 1 g 0.8Ag A f P + ' 6 Based on principle tensile stress exceeding ft = 6 c f ' Accounts for degradation due to flexural and bond cracks Degrades both Vs and Vc based on ductility Sezen and Moehle, 2004

Shear Strength FEMA 356 ACI 318-05 Displacement Ductility Sezen and Moehle, 2004

Shear Strength Priestley et al., 1994 FEMA 273 Displacement Ductility Sezen and Moehle, 2004

Column response Effective Stiffness Strength Drift Capacities

Shear Failure Shear capacity V Flexural capacity Drift or Ductility m + s m - s m + s m - s Flexural capacity Large variation in response Drift or Ductility Elwood and Moehle, 2005a

Shear Failure V High axial load Low axial load Drift or Ductility Drift at shear failure Elwood and Moehle, 2005a

Drift at Shear Failure Model Drift capacity depends on: amount of transverse reinforcement shear stress axial load 4 Elwood and Moehle, 2005a

Drift at Axial Failure Model V Ps Vd dc P s Aswfy N Vsf q dc P s Aswfy N Vsf q Simplifying Assumptions V assumed to be zero since shear failure has occurred Dowel action of longitudinal bars (Vd) ignored Compression capacity of longitudinal bars (Ps) ignored FBD illustrates forces acting on the top portion of a shear damaged column V ignored due to lost lateral capacity Vd small due to large hoop spacing Ps ignored due to low buckling capacity when deformed å + = ® q sin cos sf y V N P F s dc f A st x tan m Classic Shear-Friction ÷ ø ö ç è æ - + = q m cos sin tan s dc f A P y st Elwood and Moehle, 2005b

Drift at Axial Failure Model Relationships combine to give a design chart for determining drift capacities. sw ÷ ø ö ç è æ - + = q m cos sin tan s dc f A P y st q  65º m vs. Drift at axial failure  3% Elwood and Moehle, 2005b

Drift at Axial Failure Model Elwood and Moehle, 2005b

Drift models for flexural failures Flexural strength will degrade for columns with Vp << Vo due to spalling, bar buckling, concrete crushing, etc. Several drift models have been developed: Drift at onset of cover spalling: Drift at bar-buckling: Drift at 20% reduction in flexural capacity: (Berry and Eberhard, 2004) (Berry and Eberhard, 2005) 50 for rectangular columns, 150 for spiral-reinforced columns (Zhu, 2005)

How to apply models… First classify columns based on shear strength: Vp/Vo > 1.0  shear failure 1.0 ≥ Vp/Vo ≥ 0.6  flexure-shear failure Vp/Vo < 0.6  flexure failure where

How to apply models… Shear failure V Force-controlled Define drift at shear failure using effective stiffness and Vo. May be conservative if Vp ≈ Vo Use drift at axial failure model to estimate Da/L Very little data available for drift at axial failure for this failure mode, but model provides conservative estimate in most cases. Do not use as primary component if V > Vo V Vo 12EIeff L3 Da/L drift

How to apply models… Flexure-Shear failure V Deformation-controlled FEMA 356 limit for primary component failing in shear. Flexure-Shear failure Deformation-controlled Max shear controlled by 2Mp/L Use drift at shear failure model to estimate Ds/L Use drift at axial failure model to estimate Da/L Do not use as primary component if drift demand > Ds/L V Vp 12EIeff L3 Ds/L Da/L drift

How to apply models… Flexure failure V Deformation-controlled Max shear controlled by 2Mp/L Use model for drift at 20% reduction in flexural capacity to estimate Df /L Do not use as primary component if drift demand > Df /L For low axial loads, axial failure not expected prior to P-delta collapse. For axial loads above the balance point and light transverse reinforcement, column may collapse after spalling of cover. V Vp 12EIeff L3 Df /L drift

Points to remember Models provide an estimate of the mean response. 50% of columns may fail at drifts less than predicted by the models. Drift Model Mean Dmeas/Dcalc CoV Dmeas/Dcalc Shear Failure 0.97 0.34 Axial Failure 1.01 0.39 Flexural Failure 1.03 0.27 Spalling 0.43 Bar Buckling 1.00 0.26

Points to remember Shear and axial failure models based on database of columns experiencing: flexure-shear failures uni-directional lateral loads All models except bar buckling and spalling only based on database of rectangular columns. Use caution when applying outside the range of test data used to develop the models! Shear and axial failure models are not coupled. If calculated drift at axial failure is less than the calculated drift at shear failure, assume axial failure occurs immediately after shear failure.

Application of Drift Models – Shake Table Tests Characteristics Half-scale, three column planar frame Specimen 1: Low axial load (P = 0.10f’cAg) Specimen 2: Moderate axial load (P = 0.24f’cAg) 4’-10” 6’ Objective To observe the process of dynamic shear and axial load failures when an alternative load path is provided for load redistribution

Specimen #1 – Low Axial Load Top of Column - Total Displ. Center Column Hysteresis Center Column - Relative Displ. Full Frame - Total Displ.

Specimen #2 – Moderate Axial Load Top of Column - Total Displ. Center Column Hysteresis Center Column - Relative Displ. Full Frame - Total Displ.

Axial Load Comparison Low Axial Load (Spec 1) Moderate Axial Load (Spec 2) Center Column Axial Load Time History

Application of Drift Models – Shake Table Tests P = 0.10f’cAg P = 0.24f’cAg Backbone from drift models FEMA backbone Elwood and Moehle, 2003

Application of Drift Models – Van Nuys, Holiday Inn 7-story reinforced concrete frame building (1965) Damaged during San Fernando and Northridge Earthquakes Did columns sustain axial load failures?

Application of Drift Models – Van Nuys, Holiday Inn Column C4 Properties: fy long = 496 MPa fy trans = 345 MPa f’c = 28 MPa P = 0.13 Ag f’c L = 2.08 m Direction of shear failure #2 @ 305 6 - #7 508 A A 356 Section A-A 356

Application of Drift Models – Van Nuys, Holiday Inn Fourth story column: Max. interstory drift ≥ 0.018 Interpolated from recorded motions on third and sixth floors → Lower Bound Axial load failure expected to follow rapidly after shear failure. Elwood and Moehle, 2004

Need for probabilistic model Probability of shear failure V f (Ds/L) drift Ok?

Probabilistic Drift Capacity Models Median prediction of drift at shear failure: Median prediction of drift at flexural failure: Median prediction of drift at axial failure: Now have distributions on coefficients, capturing uncertainty in model!! Zhu, 2005

Fragility curves – Shear Failure Median Median - s Drift limit Zhu, 2005

Fragility curves – Flexural Failure Median - s Drift limit Zhu, 2005

Fragility curves – Axial Failure Median - s Drift limit Zhu, 2005

Probabilistic model for drift at axial failure 1% Zhu, 2005

Application of Probabilistic Drift Capacity Model The probabilistic drift capacity model is used to develop a fragility estimate for column from Van Nuys, Holiday Inn. Confidence bounds: Based on model (epistemic) uncertainty Shear 85% confidence bound 85% confident that Pf ≤ 6.1% 15% confidence bound Pf = 3.7% Zhu et al., 2006

Application of Probabilistic Drift Capacity Model The relation between the fragility curves of shear failure and axial failure gives useful information regarding the column axial load capacity after shear failure. Zhu, 2005

Assessment of FEMA 356 Probabilistic models can be used to assess the probability of failure implied by drift limits in FEMA 356. “Shear-controlled” response Ds/L model compared with LS criteria for secondary components Da/L model compared with CP criteria for secondary components Pf = 2.6% at LS limit Fragility Pf = 0.65% at CP limit Lynn 2CLH18 LS CP Drift demand Zhu, 2005

Assessment of FEMA 356 Life Safety (shear failure) Collapse Prevention (axial failure) Level of safety provided is not consistent for all columns. Is this level of safety appropriate? Zhu, 2005

Analytical Model for Shear-Critical Columns Shear-failure model V P V Beam-Column Element (including flexural and slip deformations) Zero-length Shear Spring Zero-length Axial Spring sw da drift ds Axial-failure model P Elwood, 2004

Analytical Model for Shear-Critical Columns Test data Static analysis limit state surface sw Elwood, 2004

Benchmark Shake Table Tests NCREE, Taiwan, 2005 E-Defence, Japan, 2006 PEER, 2006

NCREE Shake Table Test 1

NCREE Shake Table Test 2

Analysis using OpenSees

Lap Splice Failures

Effect of poor lap splices Dslip P bar yield P bar pullout M D bar q D bar

Melek and Wallace (2004) Six Full-Scale Specimens 18 in. square column 8 – #8 longitudinal bars #3 ties with 90 hooks 20db lap splice Tested with Lateral and Axial Load Lateral Load Standard Loading History Near Field Loading History Axial Load Constant Melek and Wallace (2004)

Test Matrix (12-1) ACI-318-99 Melek and Wallace (2004)

Experimental Results *normalized Melek and Wallace (2004)

Observed Damage Specimen: S20MI 1.5% Drift Splice Deterioration (Fult=53 kips) 3% Drift 5% Drift 7% Drift Axial Load Capacity Lost Melek and Wallace (2004)

S10MI – S20MI – S30MI Melek and Wallace (2004)

S20MI – S20HI – S20HIN Melek and Wallace (2004)

Axial Load Capacity S20MI, S20HI, S30MI, S30XI Axial load capacity lost due to buckling of longitudinal bars 90 ties at 4” and 16” above pedestal opened up Concrete cover lost S20HIN – Axial Load Capacity Maintained Near Fault Displacement History (Less cycles) Concrete cover intact Melek and Wallace (2004)

Axial load capacity Monotonic loading Low axial load Axial capacity model assumes the column has sustained a shear failure. Not developed for splice failures and flexurally dominated columns. No axial failure

FEMA 356 lap splice provisions Adjust yield stress based on lap splice length: Cho and Pinchiera (2005) evaluated provisions using detailed bar analysis calibrated to test data.

Spring model for anchored bar lb fs Slip Bond Stress Strain Stress e y f E sh Harajli (2002) (Cho and Pincheira, 2005)

FEMA 356 lap splice provisions FEMA 356 under-predicts steel stress. 0.8 (Cho and Pincheira, 2005)

Modified Equation (Cho and Pincheira, 2005)

Modified Equation (Cho and Pincheira, 2005)

Modified Steel Stress Equation (Cho and Pincheira, 2005)

References Berry, M., Parrish, M., and Eberhard, M., (2004) “PEER Structural Performance Database User’s Manual,” (www.ce.washington.edu/~peera1), Pacific Earthquake Engineering Research Center, University of California, Berkeley. Berry, M., and Eberhard, M., (2004) “Performance Models for Flexural Damage in Reinforced Concrete Columns,” PEER report 2003/18, Berkeley: Pacific Earthquake Engineering Research Center, University of California. Berry, M., and Eberhard, M., (2005) “Practical Performance Model for Bar Buckling”, Journal of Structural Engineering, ASCE, Vol. 131, No. 7, pp. 1060-1070. Cho, J-Y, and Pincheira, J. A., (2004) "Nonlinear Modeling of RC Columns with Short Lap Splices," Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, B. C., Canada. Elwood, K.J., and Moehle, J.P., (2005a) “Drift Capacity of Reinforced Concrete Columns with Light Transverse Reinforcement”, Earthquake Spectra, Earthquake Engineering Research Institute, vol. 21, no. 1, pp. 71-89. Elwood, K.J., and Moehle, J.P., (2005b) “Axial Capacity Model for Shear-Damaged Columns”, ACI Structural Journal, American Concrete Institute, vol. 102, no. 4, pp. 578-587. Elwood, K.J., (2004) “Modelling failures in existing reinforced concrete columns”, Canadian Journal of Civil Engineering, vol. 31, no. 5, pp. 846-859. Elwood, K.J., and Moehle, J.P., (2004) “Evaluation of Existing Reinforced Concrete Columns”, Proceedings of the Thirteenth World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 2004, 15 pages. Elwood, K. J. and Moehle, J.P., (2003) “Shake Table Tests and Analytical Studies on the Gravity Load Collapse of Reinforced Concrete Frames”, PEER report 2003/01, Berkeley: Pacific Earthquake Engineering Research Center, University of California, 346 pages. Melek, M., and Wallace, J. W., (2004) "Cyclic Behavior of Columns with Short Lap Splices,“ ACI Structural Journal, V. 101, No. 6, pp. 802-811. Priestley, M.J.N., Verma, R., and Xiao, Y., (1994) “Seismic Shear Strength of Reinforced Concrete Columns,” Journal of Structural Engineering, Vol. 120, No. 8, pp. 2310-2329. Sezen, H., and Moehle, J.P., (2004) “Shear Strength Model for Lightly Reinforced Concrete Columns,” Journal of Structural Engineering, Vol. 130, No. 11, pp. 1692-1703. Zhu, L. (2005) “Probabilistic Drift Capacity Models for Reinforced Concrete Columns”, MASc Thesis, Department of Civil Engineering, University of British Columbia. Zhu, L., Elwood, K.J., Haukaas T. and Gardoni, P., (2005) “Application of a Probabilistic Drift Capacity Model for Shear-Critical Columns,” Journal of the American Concrete Institute (ACI), Special Publication.